Question: What is process of message authentication by using MAC and private key? What is an index of the output for the input message with index

What is process of message authentication by using MAC and private key?
What is an index of the output for the input message with index 1?
\table[[Initial Permutation,],[58,50,42,34,26,18,10,02],[60,52,44,36,28,20,12,04],[62,54,46,38,30,22,14,06],[64,56,48,40,32,24,16,08],[57,49,41,33,25,17,09,01],[59,51,43,35,27,19,11,03],[61,53,45,37,29,21,13,05],[63,55,47,39,31,23,15,07]]
What is process of message authentication by using MAC and private

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